CHARACTERISTICS, COVARIANCES, AND AVERAGE RETURNS: 1929-1997

[Pages:10]First draft: December 1997 This draft: February 1999

CHARACTERISTICS, COVARIANCES, AND AVERAGE RETURNS: 1929-1997 James L. Davis, Eugene F. Fama, and Kenneth R. French* Abstract

The value premium in U.S. stock returns is robust. The positive relation between average return and book-to-market equity is as strong for 1929-63 as for the subsequent period studied in previous papers. A three-factor risk model explains the value premium better than the hypothesis that the book-to-market characteristic is compensated irrespective of risk loadings.

* College of Business, Kansas State University (Davis), Graduate School of Business, University of Chicago (Fama) and Sloan School of Management, Massachusetts Institute of Technology (French). Support for data collection from Dimensional Fund Advisors and the comments of Kent Daniel, John Heaton, RenZ Stulz, Sheridan Titman, and two referees are gratefully acknowledged.

Firms with high ratios of book value to the market value of common equity have higher average returns than firms with low book-to-market ratios (Rosenberg, Reid, and Lanstein (1985)). Because the capital asset pricing model (CAPM) of Sharpe (1964) and Lintner (1965) does not explain this pattern in average returns, it is typically called an anomaly.

There are four common explanations for the book-to-market (BE/ME) anomaly. One says that the positive relation between BE/ME and average return (the so-called value premium) is a chance result unlikely to be observed out of sample (Black (1993), MacKinlay (1995)). Out-ofsample evidence is, however, provided by Chan, Hamao, and Lakonishok (1991), Capaul, Rowley, and Sharpe (1993), and Fama and French (1998). They document strong relations between average return and BE/ME in markets outside the U.S. Using a rather small sample of firms, Davis (1994) finds that the relation between average return and BE/ME observed in recent U.S. returns extends back to 1941. We extend Davis? data back to 1926, and we expand the coverage to all NYSE industrial firms. We find that the value premium in pre-1963 returns is close to that observed for the subsequent period in earlier work. These results argue against the sample-specific explanation for the value premium.

The second story for the value premium is that it is not an anomaly at all. The higher average returns on high BE/ME stocks are compensation for risk in a multifactor version of Merton?s (1973) intertemporal capital asset pricing model (ICAPM) or Ross?s (1976) arbitrage pricing theory (APT). Consistent with this view, Fama and French (1993) document covariation in returns related t o BE/ME beyond the covariation explained by the market return. Fama and French (1995) show that there is a BE/ME factor in fundamentals (earnings and sales) like the common factor in returns. The acid test of a multifactor model is whether it explains differences in average returns. Fama and French (1993, 1996) propose a three-factor model that uses the market portfolio and mimicking portfolios for factors related to size (market capitalization) and BE/ME to describe returns. They find that the model largely captures the average returns on U.S. portfolios formed on size, BE/ME, and other variables known to cause problems for the CAPM (earnings/price, cashflow/price, past sales growth, and long-term past return). Fama and French (1998) show that an international version of

their multifactor model seems to describe average returns on portfolios formed on scaled price variables in 13 major markets.

The third explanation for the value premium says it is due to investor overreaction to firm performance. High BE/ME stocks tend to be firms that are weak on fundamentals like earnings and sales, while low BE/ME stocks tend to have strong fundamentals. Investors overreact t o performance and assign irrationally low values to weak firms and irrationally high values to strong firms. When the overreaction is corrected, weak firms have high stock returns and strong firms have low returns. Proponents of this view include DeBondt and Thaler (1987), Lakonishok, Shleifer, and Vishny (1994), and Haugen (1995).

The final story for the value premium, suggested by Daniel and Titman (1997), is that it traces to the value characteristic, not risk. For example, a behavioral story that does not require overreaction is that investors like growth stocks (strong firms) and dislike value stocks (weak firms). The result is a value premium (low prices and high expected returns for value stocks relative t o growth stocks) that is not due to risk. The behavioral overreaction story can also be viewed as a variant of the characteristics model. In general, the model covers anything that produces a premium for the value characteristic relative to the growth characteristic and is not the result of risk.

Daniel and Titman (1997) argue that past research cannot distinguish the risk model from the characteristics model. The problem is that the value and growth characteristics are associated with covariation in returns. For example, industries move through periods of distress and growth. When portfolios are formed to capture a risk factor related to relative distress, they pick up return covariation within industries that is always present but for the moment happens to be associated with growth or distress. In this view, the value premium seems to be related to the covariance of returns with a common distress factor, when in fact it is due to the growth and distress characteristics. As a result, one cannot distinguish the risk story from the characteristics story in the typical tests that focus on common factors.

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Daniel and Titman (1997) suggest a clever way to break this logjam. If characteristics (growth and distress) drive expected returns, there should be firms that have characteristics that do not match their risk loadings. For example, there should be some strong firms in distressed industries. In the characteristics model, these firms have low returns because they are strong. But they can have high loadings on a distress risk factor if the factor is in part due to covariation of returns within industries. Thus, the returns on these firms will be too low, given their risk loadings. Conversely, there are distressed firms in strong industries. Because they are distressed, they have high returns, but in terms of risk loadings they look like strong firms. If characteristics drive prices, their returns will be too high given their risk loadings.

In short, the characteristics hypothesis says that relative distress drives stock returns, and BE/ME is a proxy for relative distress. Low BE/ME (characteristic of strong firms) produces low stock returns, irrespective of risk loadings. Similarly, high BE/ME stocks (distressed firms) have high returns, regardless of risk loadings. In contrast, the risk story says expected returns compensate risk loadings, irrespective of the BE/ME characteristic. It is clear, then, that the empirical key t o distinguishing the risk model from the characteristics model is to find variation in risk loadings unrelated to BE/ME.

To identify independent variation in characteristics and risk loadings, Daniel and Titman (1997) form portfolios by triple-sorting stocks on size, BE/ME, and risk loadings. We use a similar approach, but for a much longer time period. Daniel and Titman study returns from 7/73 to 12/93, 20.5 years. Our tests cover the 7/29-6/97 period, 68 years. The extended sample period enhances the power of the tests of the characteristics model against the risk model.

Our results are easily summarized. The Daniel-Titman (1997) evidence in favor of the characteristics model is special to their rather short sample period. In our more powerful tests for 7/29-7/97, the risk model provides a better story for the relation between BE/ME and average return.

I. Summary Statistics for the Premiums Using Moody?s Industrial Manuals, we collect book common equity (BE) from 1925 to 1996 for all NYSE industrial firms that do not have BE data on Compustat. To keep the task manageable,

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we do not collect BE for financial firms, transportation firms, and utilities. To expand the sample of

firms, beginning in 1954 we merge the hand-collected data for NYSE industrials with the Compustat

data for NYSE, AMEX, and NASDAQ industrials and non-industrials.

The number of firms in our sample grows steadily through time. On the first portfolio

formation date, 6/29, we have BE data for 339 NYSE firms. By 6/53, we have 756 NYSE firms.

With the addition of Compustat data in 6/54 the sample increases to 834 NYSE firms. On the last

portfolio formation date, 6/96, the sample contains 4562 NYSE, AMEX, and NASDAQ firms with

BE data.

Like Daniel and Titman (1997), our alternative to the characteristics model is that expected

returns conform to the three-factor asset pricing model in Fama and French (1993),

E(Ri) - Rf = bi[E(RM) - Rf] + siE(SMB) + hiE(HML).

(1)

Ri is the return on asset i, Rf is the riskfree interest rate, and RM is the return on the value-weight

market portfolio. SMB is the difference between the returns on a portfolio of small stocks and a

portfolio of big stocks, constructed to be neutral with respect to BE/ME. Specifically, in June of

each year we use independent sorts to allocate the NYSE, AMEX, and NASDAQ stocks in our sample

to two size groups and three BE/ME groups. Big stocks (B) are above the median market equity of

NYSE firms and small stocks (S) are below. Similarly, low BE/ME stocks (L) are below the 30th

percentile of BE/ME for NYSE firms, medium BE/ME stocks (M) are in the middle 40 percent, and

high BE/ME stocks (H) are in the top 30 percent. We form six value-weight portfolios, S/L, S/M,

S/H, B/L, B/M, and B/H, as the intersections of the size and BE/ME groups. For example, S/L is the

value-weight return on the portfolio of stocks that are below the NYSE median in size and in the

bottom 30 percent of BE/ME. SMB is the difference between the equal-weight averages of the

returns on the three small stock portfolios and the three big stock portfolios,

SMB = (S/L + S/M + S/H)/3 - (B/L + B/M + B/H)/3.

(2)

Similarly, HML is the difference between the return on a portfolio of high BE/ME stocks and the

return on a portfolio of low BE/ME stocks, constructed to be neutral with respect to size;

HML = (S/H + B/H)/2 - (S/L + B/L)/2.

(3)

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